A cryptocurrency is a digital currency that can be exchanged online for goods and services. Cryptocurrencies are deployed over public blockchains which have the transactions duplicated and distributed across the nodes of a computer network. This decentralized mechanism is devised in order to achieve reliability in a network consisting of unreliable nodes. Privacy, anonymity and security have become crucial in this context. For that reason, formal and mathematical approaches are gaining popularity in order to guarantee the correctness of the cryptocurrency implementations. Mimblewimble is a privacy-oriented cryptocurrency technology which provides security and scalability properties that distinguish it from other protocols of its kind. It was proposed by an anonymous developer, who posted a link to a text file on the IRC channel by the name Tom Elvis Jedusor (french name for Voldemort) in mid-2016. Mimblewimble’s cryptographic approach is based on Elliptic Curve Cryptography which allows to verify a transaction without revealing any information about the transactional amount or the parties involved. Mimblewimble combines Confidential transactions, CoinJoin and cut-through to achieve a higher level of privacy and security, as well as, scalability. In this thesis, we present and discuss these security properties and outline the basis of a model-driven verification approach to address the certification of the correctness of the protocol implementations. In particular, we propose an idealized model that is key in the described verification process. The main components of our idealized model are transactions, blocks and chain. Then, we identify and precisely state the conditions for our model to ensure the verification of relevant security properties of Mimblewimble. In addition, we analyze the Grin and Beam implementations of Mimblewimble in their current state of development. We present detailed connections between our model and their implementations regarding the Mimblewimble structure and its security properties.